Gifts Fixing

1000ms

262144K

Description:

You have $$$n$$$ gifts and you want to give all of them to children. Of course, you don't want to offend anyone, so all gifts should be equal between each other. The $$$i$$$-th gift consists of $$$a_i$$$ candies and $$$b_i$$$ oranges.

During one move, you can choose some gift $$$1 \le i \le n$$$ and do one of the following operations:

eat exactly one candy from this gift (decrease $$$a_i$$$ by one);
eat exactly one orange from this gift (decrease $$$b_i$$$ by one);
eat exactly one candy and exactly one orange from this gift (decrease both $$$a_i$$$ and $$$b_i$$$ by one).

Of course, you can not eat a candy or orange if it's not present in the gift (so neither $$$a_i$$$ nor $$$b_i$$$ can become less than zero).

As said above, all gifts should be equal. This means that after some sequence of moves the following two conditions should be satisfied: $$$a_1 = a_2 = \dots = a_n$$$ and $$$b_1 = b_2 = \dots = b_n$$$ (and $$$a_i$$$ equals $$$b_i$$$ is not necessary).

Your task is to find the minimum number of moves required to equalize all the given gifts.

You have to answer $$$t$$$ independent test cases.

Input:

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The first line of the test case contains one integer $$$n$$$ ($$$1 \le n \le 50$$$) — the number of gifts. The second line of the test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the number of candies in the $$$i$$$-th gift. The third line of the test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^9$$$), where $$$b_i$$$ is the number of oranges in the $$$i$$$-th gift.

Output:

For each test case, print one integer: the minimum number of moves required to equalize all the given gifts.

Sample Input:

5
3
3 5 6
3 2 3
5
1 2 3 4 5
5 4 3 2 1
3
1 1 1
2 2 2
6
1 1000000000 1000000000 1000000000 1000000000 1000000000
1 1 1 1 1 1
3
10 12 8
7 5 4

Sample Output:

Note:

In the first test case of the example, we can perform the following sequence of moves:

choose the first gift and eat one orange from it, so $$$a = [3, 5, 6]$$$ and $$$b = [2, 2, 3]$$$;
choose the second gift and eat one candy from it, so $$$a = [3, 4, 6]$$$ and $$$b = [2, 2, 3]$$$;
choose the second gift and eat one candy from it, so $$$a = [3, 3, 6]$$$ and $$$b = [2, 2, 3]$$$;
choose the third gift and eat one candy and one orange from it, so $$$a = [3, 3, 5]$$$ and $$$b = [2, 2, 2]$$$;
choose the third gift and eat one candy from it, so $$$a = [3, 3, 4]$$$ and $$$b = [2, 2, 2]$$$;
choose the third gift and eat one candy from it, so $$$a = [3, 3, 3]$$$ and $$$b = [2, 2, 2]$$$.

Informação

Provedor Codeforces

Código CF1399B